Virtual particles

[FireGarden]

As required for Hawking radiation.
What proof do we have for them? Or are they entirely theoretical?

Is there any evidence that the energy level of a vacuum fluctuates in any way? (What would "fluctuate" mean anyway? What time scale?)

I will be studying QM this year, but I'm currently pretty ignorant about it.

[Tez]

Get the book "The quantum vacuum" by Peter Milonni from the library. Will give you a good overview of the myriad effects that are due to vacuum fluctuations - from the lamb shift in atoms to the casmir effect to Unruh radiation (similar to Hawking radiation).

[garys_2k]

One of the earliest physical proofs of vacuum fluctuations was measurement of the Casimir Effect and the measurement's agreement with theory.

Read about it HERE (http://physicsweb.org/article/world/15/9/6) for a good explanation and why it validates the vacuum fluctuation. Machines have been built that exploit the Casimir Effect and it has to be taken into account when fab'ing microchips.

[digitoxin]

Since the wave function of qm is not defined for times that are smaller than one period (because then its not a wave yet), particles can appear if they disappear before the time of one period. Its the same thing as the Heissenberg correlation, all in all, where you cant localize the position of a wave below one wavelength because the wave function (according to the fourier transform) becomes a continous spectrum instead of a fixed number then.

The time scale can therefore be calculated from the wave function of the specific particle.

[FireGarden]

Thanks Tez, garys_2k
That's a good start to some research.
So the Casimir effect has been observed (it's the first time I've heard of a force that's proportional to 1/distance^4) and that provides support for vacuum fluctuations.

That's still not quite the same as particles appearing out of the vacuum. (Although, of course, you could say that energy and matter are interchangeable)

Thanks digitoxin,
But that was way too technical for me. I'll read what you said again at the end of the year. Or next year maybe.... (But thanks) ... Or you could try again.

[digitoxin]

Ok another try:

According to the uncertainty principle (Heissenberg), time and energy cannot be measured exactly at the same time. For long time periods (normal physical reality), the energy is well defined. However, for very small time periods, the energy becomes uncertain. That means that particles can appear out of the nothing. However, their lifetime is limited by the amount of uncertainty. So they have to dissapear before their energy would become "certain", and that is what they do.
It follows that those particles can never be measured, but some theories make use of their existance.

[BillyJoe]

Originally posted by digitoxin
.....for very small time periods, the energy becomes uncertain. That means that particles can appear out of the nothing. However, their lifetime is limited by the amount of uncertainty. So they have to dissapear before their energy would become "certain".... But isn't quantum fluctuation just a logical deduction from the uncertainty principle......

(1) The energy of a system is always uncertain.
(2) Zero is certain.
(3) Therefore, the energy of a system can never be zero.

Hence the quantum fluctuation in "empty space".

[FireGarden]

Thanks, digitoxin
That answers my original question: We have no proof of virtual particles.
(But we do have evidence, since the Casimir effect is good evidence of vacuum fluctuations and virtual particles would be an extension to that.)

Obviously no-one has detected Hawking radiation yet, but wasn't there something about miniature Black Holes made at the time of the Big Bang that would just about now be "evaporating"? For ~1/10th of a sec the flash should be as bright as the sun, but coming from a very small volume. (And, very probably, a long way off)

Apparently, this phenomenon isn't a candidate to explain cosmic ray bursters anymore. I don't know why.There is an upper limit on the brightness of accretion for a given radius, so surely something this bright and small has very few explanations.

[A black Hole would have to have a mass < ~10^22 Kg in order to radiate out more than the cosmic background radiation would radiate in. And a Black hole formed at the time of the Big Bang with a mass ~ 10^11 Kg could possibly be at the point of "evaporating" away. - - From Open University S357]

[garys_2k]

Originally posted by GoodPropaganda

Obviously no-one has detected Hawking radiation yet, but wasn't there something about miniature Black Holes made at the time of the Big Bang that would just about now be "evaporating"? For ~1/10th of a sec the flash should be as bright as the sun, but coming from a very small volume. (And, very probably, a long way off)

Here's a Nature article that shows we might be close to observing microscopic black holes in the laboratory:

CERN to spew black holes
Mini black holes could reveal hidden dimensions of space.
02 October 2001
PHILIP BALL

Physicists at may soon be manufacturing copious quantities of black holes. When the Large Hadron Collider (LHC) at CERN, the European particle physics laboratory near Geneva, is completed in 2005, it could produce a black hole every second.

These tiny, fleeting phenomena might just give researchers a long-sought glimpse of the hidden dimensions of space.

http://www.nature.com/nsu/011004/011004-8.html

[rwald]

I think they recently discovered the real cause for gamma ray bursts...I read about it briefly in Scientific American (I don't remember which issue; in the past couple of months)...I think it didn't involve black holes at all (though it might have involved neutron stars)...I'm too lazy at the moment to find a link, but I may be back...

[FireGarden]

garys_2k,
That was an interesting article.
The physicist Stephen Hawking predicted in the 1970s that black holes would evaporate by radiating away their energy. For astrophysical black holes this is a very slow process, but extremely small black holes should last about as long as a snowflake in hell.

[...]
This would also confirm Hawking's prediction, which has never yet been put to the test.
But what if he's wrong?!!!! :eek:
What if black holes can only get heavier?
I suppose we'll find out in 2005. Talk about putting you money where your mouth is!

rwald,
From what I could find, I don't think anyone knows what the real cause for gamma ray bursters is.

http://antwrp.gsfc.nasa.gov/diamond_jubilee/papers/pac/debate.html
It seems that G-ray bursters could be so far away that they'd have to be extraordinarily bright. That probably rules out any small source since I think there is a limit to how bright an object of given mass can be. (Eddington luminosity:: the maximum luminosity of a gravitationally bound object - any brighter and the outward radiation pressure would overcome the graviational force holding the object together.) But I suppose if it's flinging itself apart, then it can overcome that limit....???

[Underemployed]

There have been a few SF stories about tiny black holes. I believe Larry Niven wrote one about a crew of explorers who found one in an alien lab on Mars. It was used to create gravitational waves for long-range communication.

The twist in the story was that the mini-hole was let 'loose' by one of the characters when his arch-rival was directly under it. Black hole zooms down into the planet, killing rival in the process. It ended with the killer getting off scott-free as no murder weapon could be found :rolleyes: and Mars doomed to be swallowed up in a few months as the hole got bigger.

It seems we are just going to have to hope that Hawking was right about tiny black holes if they really are going to be created by the bucketful in 2005. :eek:

[rwald]

Here's the article about gamma-ray bursts:

http://www.sciam.com/article.cfm?articleID=00056F3D-4B5A-1DC8-AF71809EC588EEDF&pageNumber=1&catID=2

It reads like they now know the source of most GRBs...

[garys_2k]

Originally posted by GoodPropaganda
garys_2k,
That was an interesting article.

But what if he's wrong?!!!! :eek:
What if black holes can only get heavier?
I suppose we'll find out in 2005. Talk about putting you money where your mouth is!


I thought a bit about that and am hoping that the first time they power up the collider with enough energy to theoretically create black holes they watch VERY carfully for Hawking radiation. Not seeing any would, I'd hope, be a giant red flag to halt further work at that power level to try to detect if any non-evaporating black holes had been produced.

I would assume that a two-proton mass black hole would likely be captured in any shielding surrounding the accelerator's collision zone, where it would occasionally swallow electrons or nucleii from the metal (lead?) of the shield itself. These events should cause some sort of radiative emission, perhaps a wisp of gamma radiation.

If THAT is detected I would hope that those shields would be dismatled and hustled to a rocket capable of propelling them outside of the solar system. Having a stable black hole anywhere nearby would eventually destroy us.

It would likely take months to consume enough material to eat its container, and hopefully by then it would have achieved sun escape velocity and be well on its way. I'd HOPE it would get through the asteroid and kupier belts without incident and could join Pioneer 10 on a long, long ride.

Of course, they WILL demonstrate Haking is right, the holes WILL decay on schedule and we'll get a lot of science. I just hope they have thought of the necessary alternatives.

[FireGarden]

garys_2k
It still seems to be a bizzarely dangerous way to start research on black holes. If all that exists to show that Hawking is right are paper calculations, then conducting this research has to be an act of faith. That the calculations are based on theories that are supported by strong evidence is merely indirect evidence that the extensions to those theories are correct.


Underemployed
And garys_2k has provided another SF scenario in which the inhabitants of the Alpha Centauri system come here to get compensation for the black holes we've dumped in their back yard!! :)


rwald
thanks for the link.
So GRBs don't radiate equally in every direction, so the total energy radiated isn't what you might initially expect from their apparent brightness from our direction.

[PixyMisa]

Actually, teeny-weeny black holes aren't much of a problem, even if somehow they don't evaporate spontaneously. They're so small they can only swallow one subatomic particle at a time, and only if it hits the black hole dead on. They don't suck stuff in because their gravity is negligible even at an angstrom's distance.

And if they don't spontaneously evaporate, then there'll be some floating around already from various big and nasty explosions (including but not limited to the big bang itself). So we add a few more to the mix - the Earth's doomed in a few billion years anyway.

[Underemployed]

Well that's alright then.

Before the first Nuke was tested at Los Alamos, many eminent physicists fortold the end of the world as an explosion of that magnitude would ignite the atmosphere and cover the whole world in a burning sky.

A bit like the clever fellows who laughed at the idea of humans travelling faster than 30mph as the forces would tear us apart.

It still sounds like a bad idea to deliberately create black holes though...

[PixyMisa]

Originally posted by Underemployed
Before the first Nuke was tested at Los Alamos, many eminent physicists fortold the end of the world as an explosion of that magnitude would ignite the atmosphere and cover the whole world in a burning sky.They were wrong. I'd have to do quite a bit of digging to be able to say whether they should have known that or not.A bit like the clever fellows who laughed at the idea of humans travelling faster than 30mph as the forces would tear us apart.Well, I don't think anyone ever suggested that. It was suggested that people would suffocate, which is sufficiently stupid.It still sounds like a bad idea to deliberately create black holes though... The point is, if these mini-black holes were going to cause disaster, the Earth would already be gone, because the Universe is full of natural particle accelerators.

[rwald]

Pixy, if the universe is full of "natural particle accelerators," than why do scientists often say they're recreating substances which haven't existed since the Big Bang? Hyperbole?

Also, even if these deadly miniature black holes were being created all the time, it wouldn't necessarily matter, as they would just devour a solar system or two, and then sit happily as a normal black hole. There's no reason to say that they'd have caused any effect we'd currently see.

For the record, I agree with your opinion that miniature black holes are harmless. I'm just pointing out some possible flaws in your arguments.

Originally posted by PixyMisa
They don't suck stuff in because their gravity is negligible even at an angstrom's distance.


Thank heavens for that good ol' inverse square law.

[FireGarden]

Oh what a waste.
I've just spent my life savings building a black hole proof shelter, and NOW PixyMisa tells me....

Since mini black holes interact so weakly with everything, I'd suppose that their distribution after the big bang should be fairly uniform (like the background radiation) which would imply that they're temporary (non-left to see, and they haven't grown after billions of years of light snacking) or very rare (non-nearby, but then the expansion of the universe would have put huge distances between them).

The black holes that (probably) exist can be accounted for by other means, I'd expect more if such "easily" produced phenomena lasted forever. (And on the assumption that billions of years is enough time for theses minis to grow into macros - if not, then who cares?)

So mini black holes are probably temporary. Who needs Hawking radiation to realise that? :)

A convincing argument Pixy!
Who's going to change my state of mind back to abject terror?

[Underemployed]

Well, I'm convinced! Make all the singularities you want.

They will probably make great novelty gifts too.

[FireGarden]

Originally posted by Underemployed
Well, I'm convinced! Make all the singularities you want.

They will probably make great novelty gifts too.

:D :D :D

rwald
Also, even if these deadly miniature black holes were being created all the time, it wouldn't necessarily matter, as they would just devour a solar system or two, and then sit happily as a normal black hole.
But the question is,
What happened to all those mini black holes created in the big bang? They should have been as evenly distributed as all the radiation. (Or atleast as evenly as the matter). And if they can make them by the bucketload at CERN, then how many did the BB make?

If they can't get smaller, they have to get bigger. And just the background radiation must be enough to feed them so that they get pretty big after billions of years. Otherwise (if they grow even more slowly than that) you could right them off as dark matter. But in that case, surely they grow too slowly to be dangerous within the lifetime of Earth.

[rwald]

I'm not suggesting that any of the primordial miniature black holes would be a hazard to Earth. I'm just postulating that they might exist, but be so remote from Earth that we can't detect them.

In other words, the existing ones are harmless. But if we were to create another one in this solar system...let's just hope we've already got everything packed.

Of course, if they would have grown so large as to be unavoidable, than my whole line of reasoning is shot. Is that the case?

[Soapy Sam]

There's one in my washing machine. Quite small. Only swallows one sock at a time.

[PixyMisa]

Originally posted by rwald
Pixy, if the universe is full of "natural particle accelerators," than why do scientists often say they're recreating substances which haven't existed since the Big Bang? Hyperbole?Guess so. Considering the energies of some of the cosmic rays we've detected (like the notable one that arrived with the energy of an incoming baseball) I'd say that they mean these particles haven't existed in quantity since the big bang.

Hmm. On the other hand, a lot of these particles are very very short lived, so even if they're being created by your favourite big exploding thing (I like neutron star collisions myself) we still wouldn't see them.Also, even if these deadly miniature black holes were being created all the time, it wouldn't necessarily matter, as they would just devour a solar system or two, and then sit happily as a normal black hole. There's no reason to say that they'd have caused any effect we'd currently see.Well, if they're being created in volume - and they certainly would have been in the big bang if not later - and they don't go pfft of their own accord, then there'd already be a whole bunch of them inside the Earth, nibbling away these past four billion years. These things aren't like stellar black holes; they're sub-microscopic in mass and sub-atomic in size. The big bang would have created not just a few of them, but boatloads all over the place.For the record, I agree with your opinion that miniature black holes are harmless. I'm just pointing out some possible flaws in your arguments. Is cool.

[PixyMisa]

Originally posted by rwald
IOf course, if they would have grown so large as to be unavoidable, than my whole line of reasoning is shot. Is that the case? Well, our best theory is that they go pfft. If they don't go pfft, they grow very very slowly even if they're sitting inside solid matter, let alone in open space. I'd have to check - and maybe even do some maths - but I'm not sure that even 15 billion years would allow a non-pfft mini black hole to grow to appreciable size in most circumstances.

You could cheat and drop one into a neutron star, I guess. But that doesn't increase the hazard level a whole lot.

[rwald]

So, if they didn't go pfft, then they would still not be noticible. So how do you know they go pfft?

(I know, Hawking radiation and all that, but still.)

[FireGarden]

rwald
I'm not suggesting that any of the primordial miniature black holes would be a hazard to Earth. I'm just postulating that they might exist, but be so remote from Earth that we can't detect them.
There's every chance that they do exist. The primordial minis would have ranged in size to way larger than CERN will ever produce, so some should still be around whether Hawking is right or wrong.

But are they getting bigger or smaller?
The danger was that Hawking might be wrong about them evaporating. If that were the case then surely they'd be getting bigger, and all of them should be quite big by now - no matter how small they were at the start.

But there's no evidence of them.
In other words, the existing ones are harmless. But if we were to create another one in this solar system...let's just hope we've already got everything packed.
But as I've said, either they grow too slowly to be dangerous or else they evaporate. Unless the stuff they make at CERN are a different breed. Grow quick, immortal little horrors......


EDIT:
Doh!
Writing off-line means losing the flow of conversation!

[rwald]

Basically, what I've been saying all along is that the minis may grow, and even if their growth rate is small enough that the primordial ones have had little effect on the universe, that a mini suddenly appearing in a lab on Earth could wreck havoc.

Is it just a matter of the numbers not correlating with one another? Would any black hole powerful enough to damage Earth also be powerful enough to damage the universe, given 13.7 billion years?

[PixyMisa]

Originally posted by rwald
Basically, what I've been saying all along is that the minis may grow, and even if their growth rate is small enough that the primordial ones have had little effect on the universe, that a mini suddenly appearing in a lab on Earth could wreck havoc.

Is it just a matter of the numbers not correlating with one another? Would any black hole powerful enough to damage Earth also be powerful enough to damage the universe, given 13.7 billion years? It's not a question of a primordial black hole damaging the universe; it's a question of squillions of them eating everything in sight. Either they went pfft or they don't eat very fast, 'cause the Universe is still there.

The point being that the big bang would have created mini black holes in vast quantities, and if they were going to eat the world, it would have been eaten by now.

[rwald]

Yes. So, what's to say that "they don't eat very fast" means that they're slow enough to not destroy the universe, but still fast enough to destroy the Earth? Is that possible?

[PixyMisa]

Originally posted by rwald
Yes. So, what's to say that "they don't eat very fast" means that they're slow enough to not destroy the universe, but still fast enough to destroy the Earth? Is that possible? No. When I say they eat slowly, I mean slowly. Today, an electron. Tomorrow, maybe, another electron. And now our little black hole has an electric charge which repels electrons unless they're moving fast and hit it dead on. You're still thinking in terms of stellar black holes. These things don't eat so much as have to be force-fed.

Of course, I could be wrong, in which case the world will end and you can say "I told you so!"

[PixyMisa]

Another point is that if the experiment does create black holes and they are stable, they will be the smallest and slowest-growing ones, the ones created in the largest quantities in the big bang.

[rwald]

I know what you mean. But what if the theory's wrong? What if they eat at a faster rate? Would it be hypothetically possible for the black hole to somehow eat fast enough to do damage to the Earth, but not eat fast enough to have done damage to the universe (since clearly, no such damage was done)?

[PixyMisa]

As far as I know - I'm not Stephen Hawking - no.

Given the energy levels of the CERN accelerator and the big bang, if the black holes we create now could do any harm we wouldn't be here in the first place. There would have been mini black holes inside the Earth when it first formed, and if they were harmful they would have eaten it by now.

Either black holes aren't created at these energy levels (which would be interesting), or
They go pfft (which would confirm current theory), or
They're harmless.

[rwald]

OK. That's all I've been asking.

As far as the "black holes would have been created inside the Earth" comment: Since the Earth was formed some time after the big bang, why would it have still had some primordial black holes in it? Perhaps by the time the Earth was forming, any primordial black holes would have grown too large for a solar system to successfully formed around them. In other words, by the time the Earth formed, any primordial black holes would have destroyed the solar system, therefore there aren't any primordial black holes around.

Of course, my analysis shows a complete lack of understanding of the mathematics involved. Since my highest level of mathematical knowledge is Calculus I, I guess I shouldn't keep arguing mathematical points...

Oh well. I've got to learn somehow, and I have to goad you into explaining everything to me, than so be it. ;)

[PixyMisa]

Originally posted by rwald
OK. That's all I've been asking.

As far as the "black holes would have been created inside the Earth" Not created inside the Earth. If they'd been hanging around, we'd have got a share, that's all.comment: Since the Earth was formed some time after the big bang, why would it have still had some primordial black holes in it? Perhaps by the time the Earth was forming, any primordial black holes would have grown too large for a solar system to successfully formed around them. In other words, by the time the Earth formed, any primordial black holes would have destroyed the solar system, therefore there aren't any primordial black holes around.Well, yes. That works too. Remember, there would have been lots and lots and lots and lots of primordial black holes - if they can be created at the energy levels CERN will be generating. If they grew big enough to destroy solar systems, then there would be no stars at all.Of course, my analysis shows a complete lack of understanding of the mathematics involved. Since my highest level of mathematical knowledge is Calculus I, I guess I shouldn't keep arguing mathematical points...

Oh well. I've got to learn somehow, and I have to goad you into explaining everything to me, than so be it. ;) I'm not actually doing any maths; I haven't done any serious calculus for years. The hardest stuff I do these days is 3d trig and linear algebra.

I looked up that record cosmic ray - it had an energy of about 10²⁰ eV whereas CERN is talking about, what, 10¹²? (I'd do some more digging, but the web is s-l-o-w for some reason.) So, the natural Universe is already hitting us with stuff worse than anything we can make ourselves. The advantage of making it ourselves is that it's a controlled process and much easier to study.

[garys_2k]

Alright, so is this what we're saying?

- The energy levels projected at CERN are no big deal, nature gives us more energetic collisions all the time, possibly here on earth. If a natural process (eg cosmic rays) does create black holes then we'd likely already had some created here and, since we're still around, they are either harmless or evaporate.

- The big bang would've created many, many mini black holes, so many that, if they were stable, we'd have inherited some, or possibly our sun would've, and that's still here, too. Plus, we don't see stars imploding on a routine basis so that's another good sign.

Another question: Would these mini black holes get created in a supernova? I know they create one mutha' of a shockwave but then collapse to neutron stars, but are those energy levels comparable?

How about the area surrounding a BIG black hole? I'd assume lots and lots of minis would be created there, as those particles are wound up to really high energy levels.

In any case I guess we very likely don't have anything to worry about. Thanks.

[PixyMisa]

Originally posted by garys_2k
Alright, so is this what we're saying?Yep :)Another question: Would these mini black holes get created in a supernova? I know they create one mutha' of a shockwave but then collapse to neutron stars, but are those energy levels comparable?Supernovas are pikers compared to the really big explosions. Or to put it another way: I don't know off hand if supernovas reach the necessary energy levels; I don't think so but I'd have to check.How about the area surrounding a BIG black hole? I'd assume lots and lots of minis would be created there, as those particles are wound up to really high energy levels.Hmm. Accretion disks emit x-rays, which are way down the energy scale from what we're talking about. Besides which, the point were particles near a black hole get wound up to really high energy levels is just before they get sucked into the black hole. At which point it doesn't really matter a whole lot if they got turned into mini black holes anyway.

Now, if you want to talk about colliding black holes, I'd say you have a goer.

Anyway, all of this assumes that the mini black holes don't just go pfft in the first place, something I'm not equipped to argue with Stephen Hawking about.

[garys_2k]

Thanks! :)

[FireGarden]

PixyMisa

Well, our best theory is that they go pfft. If they don't go pfft, they grow very very slowly even if they're sitting inside solid matter, let alone in open space. I'd have to check - and maybe even do some maths - but I'm not sure that even 15 billion years would allow a non-pfft mini black hole to grow to appreciable size in most circumstances.

I've tried to find an estimate for the doubling time of the mass of a black hole based on some equations used for stellar-galactic nuclei black holes. Obviously, sub-atomic black holes would need different equations - but I can't find them!

In a spherically symmetrical accretion model there is a limit called the Eddington accretion that is a maximum. (This rate can actually be exceeded in other models). From "Intro to active galactic nuclei" by BM Peterson, equation (3.11), the maximum accretion rate for a solar mass black hole is about 1.4*10^18 grams per sec. This maximum rate is proportional to the mass of the black hole, so at double mass the rate is double and hence the doubling time is constant.

1.99*10^33 grams(mass of sun) over
1.4*10^18 grams per sec

equals 1.4*10^15 sec
equals 45 million years

So in 4.5 billion years, it could have doubled at most about 100 times.
2^100 ~ 10^30

Obviously, it's unlikely that a large black hole could sustain this rate for long. But a mini black hole is more likely to be surrounded by enough matter to manage this rate. Because, for them, the rate is small. (Again, the rate may not apply because of quantum effects etc. Maybe a mini black hole can not absorb light above a certain wavelength (blind guess), in which case the background radiation may not be a source of energy to absorb except when it was a lot hotter).

Coincidently,
an electron is about 10^-30 kg, so doubled 100 times becomes ~ 1 Kg in 4.5 billion years.

So by the time the solar system has formed it could be quite large, and embedded in the Earth for another 4.5 billion years it gets even bigger. (In fact the Earth is only ~10^24 Kg)


(more) Disclaimers
Huge approximations and assumptions etc. This is only a guess. I'm a bit rushed too, so apologies for any numerical errors.

[Apologies if I'm off topic by now, I've missed alot by being off line]

[garys_2k]

Well, in any case, if the projected "will swallow the earth" timeline is about five billion years or so, I think we'll have other things to worry about by then and will likely have abandonded the earth. The sun will be advancing to later middle age by then and will likely have heated things up here to the uninhabitable level by that time.

[PixyMisa]

GoodPropaganda -

I don't think the rules for stellar black holes can be scaled down to mini black holes. You're talking about an accretion model, whereas with a mini black hole we're talking about individual quantum events.

But I don't have a mathematical treatment of the growth of mini black holes handy either. So I'm kind of stuck with the argument that if they were going to cause problems we'd already be dead...

edited to add:

Unless, of course, I want to undertake the work to produce an analysis which will probably be flawed anyway :(

[garys_2k]

Originally posted by PixyMisa
GoodPropaganda -

But I don't have a mathematical treatment of the growth of mini black holes handy either. So I'm kind of stuck with the argument that if they were going to cause problems we'd already be dead...

edited to add:

Unless, of course, I want to undertake the work to produce an analysis which will probably be flawed anyway :(
The point that any mini bh would likely initially swallow mostly electrons is a good one. They're a lot more abundant (probabalistically, anyway) and after eating more than a few that bh would develop quite a negative charge, repelling further electronic interaction (or other black holes).

I suppose that charge could make it a bit more attractive to nuclei, but I don't know how likely they'd be to run into a meaningful number of either bare nuclei (probably very rare outside of some plasmas) or even postive ions (that likely wouldn't give real access to the nucleus in any case).

It would seem to be hard to add these effects to any mathematical model.

[FireGarden]

PixyMisa
I don't think the rules for stellar black holes can be scaled down to mini black holes. You're talking about an accretion model, whereas with a mini black hole we're talking about individual quantum events
It was the best model I could find. :)
Of course classical physics would say that nuclear reactions shouldn't be going on in the sun (at least, not at the same rate). But they do because the protons don't need as much energy to get together as classical physics would demand. In view of that, I would feel it's more likely that QM effects would speed up accretion to a mini black hole rather than slow it down. But I don't know.

I was just trying to put a rough, ball-park estimate on the numbers.


garys_2k
The point that any mini bh would likely initially swallow mostly electrons is a good one.
For a black hole inbedded in the Earth, I'd agree.
Most protons are sheilded inside atoms and ions with many electrons, so an Earth born mini BH would eat very little other than electrons and become negatively charged.

But before decoupling (~300,000 years after the BB) all of the hydrogen would have been ionised. Also, and this is why I keep mentioning the background radiation, the energy density of radiation was greater than that of matter. So primordial black holes should have had an easier time eating up radiation rather than electrons/protons etc. (Which makes, incidentally, the maximum accretion equations that my numbers above are based on become totally meaningless. That's because they're based on the maximum luminosity of a matter-accreting sphere. Any brighter, and it starts to blow away matter more powerfully than it attracts it gravitationally. I don't know how to modify them to account for greater accretion of radiation than matter).

In summary
Either mini BHs weren't created in the BB in anything like the numbers you'd expect given that CERN is about to make one a day.

Or there is a QM effect that seriously slows down how quickly they can grow, and so they are still too small to notice

Or else, Hawking is right and the smallest, most numerous of the primordial BHs have evaporated.

[PixyMisa]

Your point about the energy density shortly following the big bang is a good one. There are a lot of factors to take into account, aren't there?

But yes, the summary remains the same.